Analytical considerations of the load‐deflection behavior in fibers during a filament winding process

Abstract Filament winding is a manufacturing process used in the construction of fiber composite structures, where a thermoset resin impregnated bunch of fibers is deposited on a rotating mandrel. The evolving stress and strain states due to thermal and mechanical loads during the manufacturing process are of particular interest to avoid subsequent failure of the parts. In this first approach, the mechanical load within the fiber, mainly driven by the pre‐stressed fiber tension, is investigated. Thus, the development of the fiber tension and the pressure on the mandrel as a function of the number of windings is examined. Therefore, models based on the theory of large and small deformations are derived under certain assumptions, resulting in a boundary value problem. In case of large deformations, the boundary value problem using a three‐dimensional formulation based on incompressible, isotropic hyperelasticity does not yield a simple solution. Using a small deformation formulation on the basis of a one‐dimensional consideration an analytical solution can be found. The problems are described in curvilinear coordinates. From the derived models, the required quantities including the fiber tension, the pressure on the mandrel, also as a function of the number of windings, and the fiber elongation can be calculated.