Filament-wound composites are replacing metals as the material of choice for tanks to hold liquids and gases. The composites have a high strength-to- weight ratio, making them ideal for use in aerospace and commercial ground transport. Also, the automated winding process is less expensive than other manufacturing methods for composites.

Figure 1. ABAQUS FEA Model of the end dome helical layers, showing the local fiber wind angle. Red (90°) shows hoop plies on the cylinder section

However, these tanks present several design challenges that must be addressed with nonlinear finite element analysis (FEA). Using formulae derived from materials data, nonlinear FEA verifies tank strength, stiffness, and overall performance. A typical tank design is a cylinder with a dome at either end. At least one end has a boss and a hole for filling the tank and for attaching valves, gauges, and so forth. Often, the other end has a boss as well for standing or mounting the tank.

Tank manufacture is performed by the resin impregnation of the filaments in a resin "bath" and winding of the impregnated filaments tightly in layers around a tool in the shape of the tank void. The wound fiber-resin composite is then cured under a controlled time-and-temperature profile. Once curing is complete, the tool is removed, typically through one of the end domes. Alternatively, a tank liner of sufficient structural integrity may act as the winding tool itself and remain with the composite overwrap as an integral part of the completed end product.

Figure 2. ABAQUS FEA Results showing predicted fiber strain for internal pressure load. Fiber strain computed from meridional and hoop strain using local wind angle (Fig. 1) to perform coordinate transformation.

Although composite container tanks are the same as metal tanks in function, the filament-wound tank is subject to unique tensions, stresses, and loads not seen in homogeneous isotropic materials, such as steel, and typically has a somewhat different geometric form at the tank ends. While the tank is axially symmetric, the forces on it and the thickness of material vary from end to end. Nonlinear FEA simulates each of these forces and characteristics to predict product performance and durability. There are several important analyses:

  • The designer performs a netting analysis during preliminary design. For convenience and speed, this analysis assumes the fibers form a “net,” ignoring the structural contribution of the resin matrix and assuming that all the pressure-induced tensile forces are being carried by the filaments only. The helical winding angle and the thickness of the layers of wound filaments change continuously as measured from the tangent line (parallel to the tank axis) to the filament turnaround point near the tank pole piece. The netting analysis is a good firstorder approximation of the composite material requirements for given tank specifications, but it does not capture some of the important details of solid material mechanics. The stressstiffening effect (like the tension on a violin string) and mechanical compliance of the filament-reinforced layers affect the deflection properties and load-bearing capacity of the tank wall in a nonlinear fashion, changing as a function of the winding angle and location on the tank (Figure 1).
  • Once netting analysis is complete, the designer uses nonlinear FEA to determine the mechanical response of the fiber-reinforced composite laminates. This analysis treats each composite laminate as a continuum, passing forces across the resin matrix as well as along the length of the filament. It also takes into account the nonlinear material properties as well as nonlinear geometric effects from the stress stiffening and interactions between the laminates. It should be emphasized that the FEA results are only as valid as the material properties that are provided for the analysis. These properties must include the strength and stiffness properties of the composite laminate, tank liners, pole pieces, and other features, as well as the mechanical interfaces between them. Particularly in the case of the composite laminate, deriving accurate material properties is not a trivial matter, since these properties are highly direction-dependent and can be strongly influenced by manufacturing process variables (i.e. filament tension during winding/curing, heating/cooling rates, ambient humidity, compaction pressure, resin content, void content, etc.).
  • Analysis of the end domes is critical. Ideally, the engineer creates a dome contour that allows the filament to follow geodesic paths, keeping tension uniform (isotensoid) along the length of the fibers. However, because of the curvature at the cylinder ends, and because of additional features such as bosses or gasketing surfaces, filament winding at the end domes is not purely geodesic. As a result, the designer requires nonlinear analysis to determine how the tension changes across the end domes (Figure 2). Note that much of the end dome color is constant, indicating uniform tension in the fibers, and the fiber strain increases as it approaches the polar opening.
  • The designer must also assess potential failure modes, such as through-the-thickness tensile debonding (pulling apart) within a laminate, and interlaminar shear (tearing) between laminate and liner. Designers often need to characterize these failure modes through physical prototyping and laboratory coupon testing, but it is also possible to simulate and predict them with FEA software to some degree, thereby reducing the need for physical models and speeding up the design process.

Individual tank designs may require additional analyses. For example, a cryogenic tank might include a metal liner with a different coefficient of thermal expansion than the composite material. A tank for an aerospace application may be subject to irregular vibration, pressure, and thermal loads. It may also have special stiffness and flexibility requirements. Mounting plates, bolts, gaskets, and valves on the end dome of a tank can create strong localized forces that the engineer will need to take into account.

This work was done by Daniel J. Moser, President and CTO of Compositex, and David L. Gray, General Manager of ABAQUS South. For further information, contact David Gray at 214-513-1600; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; or visit www.abaqus.com.