Direct Bundle Simulation approach for the compression molding process of Sheet Molding Compound

Abstract

The manufacturing process of Sheet Molding Compounds (SMC) induces a reorientation of fibers during the flow, which influences local properties and is of interest for structural computations. Typically, the reorientation is described with an evolution equation for the second order fiber orientation tensor, which requires a closure approximation and multiple empirical parameters to describe long fibers. However, CT scans of SMC microstructures show that fiber bundles stay mostly intact during molding. Treating hundreds of fibers in such a bundle as one instance enables direct simulation on component scale. This work proposes a direct simulation approach, in which bundle segments experience Stokes' drag forces and opposing forces are applied to the fluid field. The method is applied to specimens with a double-curved geometry and compared to CT scans. The Direct Bundle Simulation provides increased accuracy of fiber orientations and enables prediction of fiber-matrix separation with affordable computational effort at component scale.

Direct Fiber Simulation of a Compression Molded Ribbed Structure Made of a Sheet Molding Compound with Randomly Oriented Carbon/Epoxy Prepreg Strands—A Comparison of Predicted Fiber Orientations with Computed Tomography Analyses

“…Only the highly sheared strands are more likely to fan out. This observation justifies the simplifying assumption to represent thousands of carbon fibers within a strand as one bundle in order to shorten the calculation time and to enable full component scale simulations [73].…”

“…This simplification method reduces the numerical calculation time by representing thousands of fibers as fiber bundles. Considering microstructure studies reported in the literature [4,73,103,104], it can be seen that most of the fiber bundles or strands widen and flatten, but do not disperse. Only the highly sheared strands are more likely to fan out.…”

“…These statistical fiber orientation models strongly depend on empirical coefficients, which are cumbersome to determine experimentally [72,73]. Furthermore, the model simplifications and boundary condition assumptions made in these models are not valid for flexible fibers significantly longer than structural features of the part (scale separation) [21,45,73]. In addition, phenomenological models do not consider segments of one fiber being in different flow conditions (at different positions inside the material flow) at the same time, which is highly probable for long fibers [45].…”

“…Recently, Meyer et al [73] presented a DBS method that reproduces Jeffery's equation for single fiber bundles in shear flow, which are described as a chain of truss elements. Since the bundles are represented as one-dimensional instances, they can move independently from the matrix material, flow and interact through contact forces and with hydrodynamic drag forces of the surrounding flow.…”

“…Since bundle-wall and bundle-bundle interactions are considered, there is no need for empirical interaction parameters, unlike in the commonly used statistical descriptors of fiber orientation changes (Folgar-Tucker-based models). Since this DBS approach additionally considers two-way coupling it allows for a more accurate calculation of fiber volume fraction distributions, knit lines and FMS at a component level with reasonable computation times [73].…”